Most unix-like systems will have Telnet by default (some will
not have SSH believe it or not).
Also, home networks and embedded systems where the connection is localized and not towards the whole web, telnet is a simple and easy solution.
The last part is, well no offense (perhaps a bit intended) - it sounds like something coming from a person who's never used vim before.
On the day-to-day front, it cuts out repetitive tasks: like moving around the text in the conventional way, it can jump around to wherever I need without ever leaving the keyboard, searching and replacing text can be so specific, you'll wonder why people do things the way they do.
On the programming front, it's insanely powerful. It can do IDE stuff like crazy, parse directories/files with the built-in stuff, or if you really need to, regex, comparing diffs, syntax highlighting customization is unparalleled, you think that IDEs. LaTeX-suite has editing power, guess where the concepts came from. I can do my stuff in half the time with all of the shortcuts (yes, you can have pdf-preview, all the niceties of TexMaker or whatever that you're using, and have it in a GUI).
But it's not merely limited to programming use - for regular files, it's simply one of the faster and more efficient ways to edit, the fanciness can get out of the way.
Half of these posts are typed in vim. Of course, there's a learning curve. Quite honestly, I find acme to be even harder to learn, since that's a
real paradigm shift, everything about it.
It's such a braindead mentality when you have people asking why we use this schiit even though it doesn't have "shiny colors" (it can, text colors can be changed to whatever the heck you want) or "mouse support" (of course it does, gpm, visual mode, the GUI version). Yes, there's a GUI version - you compile in the support or use a package that has it compiled in. Actually, most distros have vim with GUI installed right from the start, guess that's a no-go on OS X since it doesn't bundle gtk by default.
Three more things that gets it going - it's on most if not nearly all *nix systems, portable, so you eventually learn it, this breaks some common ground since there's always exposure to it. Plus, the fact that so much software nowadays has a vi mode included (Sublime Text's vintage mode is essentially vi mode), that's just a testament to its efficiency. Last thing - it's extendable to do pretty much anything you will ever think of needing text-wise. For even more, that's emacs realm.
The thing is, use it for more than a day. It might not be for you specifically, but you can't really deny the power that it offers. It'll become very apparent once you learn beyond the surface (heck, vimtutor - it has a tutor built right in, interactive and all!)
Something more visually representative -
http://www.viemu.com/a-why-vi-vim.html
I just don't have the willpower, once I start one, it has to do something very wrong for me to drop it.
